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Bowditc¥s Remarks on Doctor Stewarfa Formula. 



cyclopedia is given the foUowiDg analytical expression of tlie fim- 

 damental theorem of Doctor Stewart's calculation, noticed in terms 



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indicating a full belief in its accuracy. "In his [Doctor Stewart's] 

 Mathematical and Physical Tracts, he has demonstrated this re- 



<i 



ark able the ore 



Let r be the 



of the moon's orbit 



** supposing it to be a circle, and tlie moon to be acted upon only 

 *^ by F, her gravity to the earth. If the mean disturbing force by 



-y 



F 



5/ 



*' which the sua diminishes the moon's gravity be/, then will ... . . 



■m 



^' the angle described by the radius vector from one apsis to the same 



"apsis be 360° x ( p~^'^ )^. This proportion which is demon- 



^' strated by Doctor Stewart in the fourth of his tracts, in a man- 

 ^'ner somewhat prolix^ on account of his rigid adherance to the 

 *' manner of ancient geometry, but in a way perfectly clear and 

 " elementary f is employed by him to deduce the mean disturbing 

 '* force from the motion of the apsides, as ascertained by observa- 

 "tion." 



After taking this historical view of the subject, which seemed 

 to be necessary in order to form a correct judgment of the present 

 state of the question, it may be remarked, that these late opinions 

 of eminent mathematicians in favour of the accuracy of this meth- 



od of computin 



of the Moon 



apsides being unac- 

 or proof, do not re- 



u^^ 



ipanied with any additional illustration or 



the objections which have been raised, that the neglect of 



L. 



tangential force and other peculiarities of 



method might 



possibly affect the result ; it therefore becomes a subject worthy of 



tt this fundamental theorem ex- 



wheth 



presses in an approximative form, the mean motion of the apsides, 



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